401 lines
10 KiB
Mathematica
401 lines
10 KiB
Mathematica
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function p = propagate_bounds_from_equalities(p)
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LU = [p.lb p.ub];
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p_F_struc = p.F_struc;
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n_p_F_struc_cols = size(p_F_struc,2);
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fixedVars = find(p.lb == p.ub & p.variabletype(:) == 0);
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if ~isempty(fixedVars)
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p_F_struc_forbilin = p_F_struc;
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p_F_struc_forbilin(:,1) = p_F_struc(:,1) + p_F_struc(:,1+fixedVars)*p.lb(fixedVars);
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p_F_struc_forbilin(:,1+fixedVars) = 0;
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else
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p_F_struc_forbilin=p_F_struc;
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end
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usedVariables = find(any(p.F_struc(:,2:end)));
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if all(isinf(p.lb(usedVariables))) & all(isinf(p.ub(usedVariables)))
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return
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end
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if p.K.f >0
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interestingRows = find(p_F_struc(1:p.K.f,1));
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if ~isempty(interestingRows)
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S = p_F_struc(interestingRows,:);
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S(:,1)=0;
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S = sum(S|S,2) - abs(sum(S,2));
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interestingRows = interestingRows(find(S==0));
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for j = interestingRows(:)'
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thisrow = p_F_struc(j,:);
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if thisrow(1)<0
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thisrow = -thisrow;
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end
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[row,col,val] = find(thisrow);
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% Find bounds from sum(xi) = 1, xi>0
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if all(val(2:end) < 0)
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usedVars = col(2:end)-1;
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if all(p.lb(usedVars)>=0)
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p.ub(usedVars) = min( p.ub(usedVars) , val(1)./abs(val(2:end)'));
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end
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end
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end
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end
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% Presolve from bilinear x*y == k
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if any(p.variabletype == 1)
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for j = 1:p.K.f
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if p_F_struc_forbilin(j,1)~=0
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[row,col,val] = find(p_F_struc_forbilin(j,:));
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% Find bounds from sum(xi) = 1, xi>0
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if length(col)==2
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val = val/val(2); % val(1) + x==0
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var = col(2)-1;
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if p.variabletype(var)==1
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[ij] = find(p.monomtable(var,:));
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if p.lb(ij(1))>=0 & p.lb(ij(2))>=0
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% xi*xj == val(1)
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if -val(1)<0
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p.feasible = 0;
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return
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else
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p.ub(ij(2)) = min( p.ub(ij(2)),-val(1)/p.lb(ij(1)));
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p.ub(ij(1)) = min( p.ub(ij(1)),-val(1)/p.lb(ij(2)));
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p.lb(ij(2)) = max( p.lb(ij(2)),-val(1)/p.ub(ij(1)));
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p.lb(ij(1)) = max( p.lb(ij(1)),-val(1)/p.ub(ij(2)));
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end
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elseif -val(1)>0 & p.lb(ij(1))>=0
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p.lb(ij(2)) = max(0,p.lb(ij(2)));
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elseif -val(1)>0 & p.lb(ij(2))>=0
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p.lb(ij(1)) = max(0,p.lb(ij(1)));
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end
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end
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end
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end
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end
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end
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A = p.F_struc(1:p.K.f,2:end);
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AT = A';
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Ap = max(0,A);ApT = Ap';
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Am = min(0,A);AmT = Am';
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two_terms = sum(p.F_struc(1:p.K.f,2:end) | p.F_struc(1:p.K.f,2:end),2)==2;
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for j = find(sum(p.F_struc(1:p.K.f,2:end) | p.F_struc(1:p.K.f,2:end),2)>1)'
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% Simple x == y
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done = 0;
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b = full(p_F_struc(j,1));
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if b==0 & two_terms(j)
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[row,col,val] = find(p_F_struc(j,:));
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if length(row) == 2
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if val(1) == -val(2)
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p.lb(col(1)-1) = max(p.lb(col(1)-1),p.lb(col(2)-1));
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p.lb(col(2)-1) = max(p.lb(col(1)-1),p.lb(col(2)-1));
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p.ub(col(1)-1) = min(p.ub(col(1)-1),p.ub(col(2)-1));
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p.ub(col(2)-1) = min(p.ub(col(1)-1),p.ub(col(2)-1));
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done = 1;
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elseif val(1) == val(2)
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p.lb(col(1)-1) = max(p.lb(col(1)-1),-p.ub(col(2)-1));
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p.lb(col(2)-1) = max(-p.ub(col(1)-1),p.lb(col(2)-1));
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p.ub(col(1)-1) = min(p.ub(col(1)-1),-p.lb(col(2)-1));
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p.ub(col(2)-1) = min(-p.lb(col(1)-1),p.ub(col(2)-1));
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done = 1;
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end
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end
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end
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if ~done
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a = AT(:,j)';
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ap = (ApT(:,j)');
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am = (AmT(:,j)');
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find_a = find(a);
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p_ub = p.ub(find_a);
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p_lb = p.lb(find_a);
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inflb = isinf(p_lb);
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infub = isinf(p_ub);
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if ~all(inflb & infub)
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if any(inflb) | any(infub)
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[p_lb,p_ub] = propagatewINFreduced(full(a(find_a)),full(ap(find_a)),full(am(find_a)),p_lb,p_ub,b);
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p.lb(find_a) = p_lb;
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p.ub(find_a) = p_ub;
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else
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[p_lb,p_ub] = propagatewoINFreduced(full(a(find_a)),full(ap(find_a)),full(am(find_a)),p_lb,p_ub,b);
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p.lb(find_a) = p_lb;
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p.ub(find_a) = p_ub;
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end
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end
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end
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end
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end
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close = find(abs(p.lb - p.ub) < 1e-12);
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p.lb(close) = (p.lb(close)+p.ub(close))/2;
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p.ub(close) = p.lb(close);
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p = update_integer_bounds(p);
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if ~isequal(LU,[p.lb p.ub])
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p.changedbounds = 1;
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end
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if any(p.lb > p.ub)
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p.feasible = 0;
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end
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function [p_lb,p_ub] = propagatewINFreduced(a,ap,am,p_lb,p_ub,b);
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%a = AT(:,j)';
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%ap = (ApT(:,j)');
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%am = (AmT(:,j)');
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%p_ub = p.ub;
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%p_lb = p.lb;
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%find_a = find(a);
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% find_a = find_a(min(find(isinf(p.lb(find_a)) | isinf(p.ub(find_a)))):end);
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for k = 1:length(a)%find_a
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p_ub_k = p_ub(k);
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p_lb_k = p_lb(k);
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if (p_ub_k-p_lb_k) > 1e-8
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L = p_lb;
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U = p_ub;
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L(k) = 0;
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U(k) = 0;
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ak = a(k);
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if ak < 0
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ak = -ak;
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aa = am;
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am = -ap;
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ap = -aa;
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b = -b;
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a = -a;
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end
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if ak > 0
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use1 = find(ap'~=0);
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use2 = find(am'~=0);
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newlower = (-b - ap(use1)*U(use1) - am(use2)*L(use2))/ak;
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newupper = (-b - am(use2)*U(use2) - ap(use1)*L(use1))/ak;
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%newlower = (-b - ap*U - am*L)/ak;
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%newupper = (-b - am*U - ap*L)/ak;
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else
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newlower = (-b - am*U - ap*L)/ak;
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newupper = (-b - ap*U - am*L)/ak;
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end
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if p_ub_k>newupper
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p_ub(k) = newupper;
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end
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if p_lb_k<newlower
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p_lb(k) = newlower;
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end
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end
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end
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p.ub = p_ub;
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p.lb = p_lb;
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function [p_lb,p_ub] = propagatewoINFreduced(a,ap,am,p_lb,p_ub,b);
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L = p_lb;
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U = p_ub;
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apU = ap*U;
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amU = am*U;
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apL = ap*L;
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amL = am*L;
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papU = ap.*U';
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pamU = am.*U';
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papL = ap.*L';
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pamL = am.*L';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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for k = 1:length(a)%find_a
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p_ub_k = p_ub(k);
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p_lb_k = p_lb(k);
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if (p_ub_k-p_lb_k) > 1e-8
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ak = a(k);
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if ak > 0
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%newlower = (-b-apU+papU(k)-amL+pamL(k) )/ak;
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%newupper = (-b-amU+pamU(k)-apL+papL(k) )/ak;
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newlower = -1e-15 + (minusbminusapUminusamL+papU(k)+pamL(k) )/ak;
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newupper = 1e-15 + (minusbminusamUminusapL+pamU(k)+papL(k) )/ak;
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else
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newlower = -1e-15 + (minusbminusamUminusapL+pamU(k)+papL(k) )/ak;
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newupper = 1e-15 + (minusbminusapUminusamL+papU(k)+pamL(k) )/ak;
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end
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if p_ub_k>newupper
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p_ub(k) = newupper;
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U(k) = newupper;
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apU = ap*U;
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amU = am*U;
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papU = ap.*U';
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pamU = am.*U';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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end
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if p_lb_k<newlower
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p_lb(k) = newlower;
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L(k) = newlower;
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apL = ap*L;
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amL = am*L;
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papL = ap.*L';
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pamL = am.*L';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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end
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end
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end
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%p.ub = p_ub;
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%p.lb = p_lb;
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function p = propagatewINF(p,AT,ApT,AmT,j,b);
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a = AT(:,j)';
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ap = (ApT(:,j)');
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am = (AmT(:,j)');
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p_ub = p.ub;
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p_lb = p.lb;
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find_a = find(a);
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% find_a = find_a(min(find(isinf(p.lb(find_a)) | isinf(p.ub(find_a)))):end);
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for k = find_a
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p_ub_k = p_ub(k);
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p_lb_k = p_lb(k);
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if (p_ub_k-p_lb_k) > 1e-8
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L = p_lb;
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U = p_ub;
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L(k) = 0;
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U(k) = 0;
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ak = a(k);
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if ak > 0
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newlower = (-b - ap*U - am*L)/ak;
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newupper = (-b - am*U - ap*L)/ak;
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else
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newlower = (-b - am*U - ap*L)/ak;
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newupper = (-b - ap*U - am*L)/ak;
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end
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% if isinf(newlower) | isinf(newupper)
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% z = newlower;
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% end
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if p_ub_k>newupper
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p_ub(k) = newupper;
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end
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if p_lb_k<newlower
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p_lb(k) = newlower;
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end
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end
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end
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p.ub = p_ub;
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p.lb = p_lb;
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function p = propagatewoINF(p,AT,ApT,AmT,j,b);
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a = full(AT(:,j)');
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ap = full((ApT(:,j)'));
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am = full((AmT(:,j)'));
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p_ub = p.ub;
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p_lb = p.lb;
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find_a = find(a);
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L = p_lb;
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U = p_ub;
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apU = ap*U;
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amU = am*U;
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apL = ap*L;
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amL = am*L;
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papU = ap.*U';
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pamU = am.*U';
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papL = ap.*L';
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pamL = am.*L';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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for k = find_a
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p_ub_k = p_ub(k);
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p_lb_k = p_lb(k);
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if (p_ub_k-p_lb_k) > 1e-8
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ak = a(k);
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if ak > 0
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%newlower = (-b-apU+papU(k)-amL+pamL(k) )/ak;
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%newupper = (-b-amU+pamU(k)-apL+papL(k) )/ak;
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newlower = (minusbminusapUminusamL+papU(k)+pamL(k) )/ak;
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newupper = (minusbminusamUminusapL+pamU(k)+papL(k) )/ak;
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else
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newlower = (minusbminusamUminusapL+pamU(k)+papL(k) )/ak;
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newupper = (minusbminusapUminusamL+papU(k)+pamL(k) )/ak;
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end
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if p_ub_k>newupper
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p_ub(k) = newupper;
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U(k) = newupper;
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apU = ap*U;
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amU = am*U;
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papU = ap.*U';
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pamU = am.*U';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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end
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if p_lb_k<newlower
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p_lb(k) = newlower;
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L(k) = newlower;
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apL = ap*L;
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amL = am*L;
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papL = ap.*L';
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pamL = am.*L';
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minusbminusapUminusamL = -b-apU-amL;
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minusbminusamUminusapL = -b-amU-apL;
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end
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end
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end
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p.ub = p_ub;
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p.lb = p_lb;
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